Landau Theory of the Crumpling Transition

An order-parameter theory of the crumpling transition in $D$-dimensional polymerized membranes embedded in $d$ dimensions is developed. Within mean-field theory, we show how self-avoidance modifies the behavior at the second-order crumpling transition. Fluctuations drive the transition first order to lowest order in $\epsilon =4-D$, for $d<\mathrm{}{d}_c\approx 219$.